<h2>DESCRIPTION</h2>

<em>v.qcount</em> computes six different quadrat count statistics that provide
a measure of how much an user defined point pattern departs from a complete
spatial random point pattern.

<p>Points are distributed following a complete spatial randomness (CSR) pattern
if events are equally likely to occur anywhere within an area. There are two
types departure from a CSR: regularity and clustering. Figure 1 gives an example
of a complete random, regular and a clustered pattern.

<!-- source of figures:
     https://github.com/OSGeo/grass-legacy/tree/releasebranch_5_4/src/sites/s.qcount/tutorial
-->

<div align="center" style="margin: 10px">
<img src="v_qcount_1.png">
<img src="v_qcount_2.png">
<img src="v_qcount_3.png">
<br>
<i>Figure 1: Realization of two-dimensional Poisson processes of 50 points on
the unit square exhibiting (a) complete spatial randomness, (b) regularity, and
(c) clustering.</i>
</div>

<p>Various indices and statistics measure departure from CSR. The
<em>v.qcount</em> function implements six different <i>quadrat count</i>
indices that are described in Cressie (1991; p. 590-591)[1] and in Ripley (1981;
p. 102-106)[2] and summarized in Table 1.

<div align="center" style="margin: 10px">
<img src="v_qcount_5.png">
<br>
<i>Table 1: Indices for Quadrat Count Data. Adapted from
Cressie [1], this table shows the statistics computed for the
quadrats in Figure 2.</i>
</div>

<p>These indices are computed as follows: <em>v.qcount</em> chooses
<b>nquadrads</b> circular quadrats of radius <b>radius</b> such that they are
completely within the bounds of the current region and no two quadrats overlap.
The number of points falling within each quadrat are counted and indices are
calculated to estimate the departure of point locations from complete spatial
randomness. This is illustrated in Figure 2.

<div align="center" style="margin: 10px">
<img src="v_qcount_4.png">
<br>
<i>Figure 2: Randomly placed quadrats (n = 100) with 584 sample points.</i>
</div>

<p>The number of points is written as category to the <b>output</b> map (and not
to an attribute table).

<h2>NOTES</h2>

This program may not work properly with lat-long data. It uses
<em>hypot()</em> in two files: <em>count.c</em> and
<em>findquads.c</em>.

<!-- TODO: add example -->

<h2>SEE ALSO</h2>

<em>
<a href="v.random.html">v.random</a>,
<a href="v.distance.html">v.distance</a>,
<a href="v.neighbors.html">v.neighbors</a>,
<a href="v.perturb.html">v.perturb</a>
</em>

<h2>REFERENCES</h2>

<b>General references include:</b>

<p>[1] Noel A. C. Cressie. <em>Statistics for Spatial Data</em>.
Wiley Series in Probability and Mathematical Statistics. John Wiley
&amp; Sons, New York, NY, 1st edition, 1991.
<p>[2] Brian D. Ripley. <em>Spatial Statistics</em>.
John Wiley \&amp; Sons, New York, NY, 1981.


<p>
<b>References to the indices include:</b>

<p>[3] R. A. Fisher, H. G. Thornton, and W. A. Mackenzie.
The accuracy of the plating method of estimating the density of
bacterial populations.
<em>Annals of Applied Biology</em>, 9:325-359, 1922.

<p>[4] F. N. David and P. G. Moore. Notes on contagious distributions in
plant populations. <em>Annals of Botany</em>, 18:47-53, 1954.

<p>[5] J. B. Douglas.  Clustering and aggregation.
<em>Sankhya B</em>, 37:398-417, 1975.

<p>[6] M. Lloyd. Mean crowding.
<em>Journal of Animal Ecology</em>, 36:1-30, 1967.

<p>[7] M. Morista. Measuring the dispersion and analysis of distribution
patterns. <em>Memoires of the Faculty of Science, Kyushu University, Series E.
Biology</em>, 2:215-235, 1959.

<p>
<b>A more detailed background is given in the tutorial:</b>

<!-- source of tutorial:
     https://github.com/OSGeo/grass-legacy/tree/releasebranch_5_4/src/sites/s.qcount/tutorial
-->

<p>[8] James Darrell McCauley 1993. Complete Spatial Randomness and Quadrat Methods - 
<a href="https://grass.osgeo.org/history_docs/v_qcount_tutorial.pdf">GRASS Tutorial on v.qcount</a>



<h2>KNOWN ISSUES</h2>

Timestamp not working for header part of counts output. (2000-10-28)

<h2>AUTHORS</h2>

<a href="http://mccauley-usa.com/">James Darrell McCauley</a>
<br>when he was at:
<a href="http://ABE.www.ecn.purdue.edu/ABE/">Agricultural Engineering</a>
<a href="http://www.purdue.edu/">Purdue University</a>

<p>Modified for GRASS 5.0 by Eric G. Miller (2000-10-28)
<br>
Modified for GRASS 5.7 by R. Blazek (2004-10-14)

<!--
<p>
<i>Last changed: $Date$</i>
-->
